Question

I don't understand this please help ​

Answer 1

350

Explanation:

The solution to the equation can be found by multiplying by the denominator, then dividing by its coefficient.

`0.22 = (77)/(x)\qquad\text{given}\\\\0.22x = 77\qquad\text{multiply by $x$}\\\\x=(77)/(0.22)=350\qquad\text{divide by the coefficient of x}`

The missing value in the fraction is 350.

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Additional comment

Here, we have rewritten the percentage as a decimal fraction. You could also rewrite it as a ratio of two integer: 22% = 22/100. Sometimes there is confusion about percentages. It can help to think of the % symbol as meaning /100:

22% = 22/100

Of course, that is "twenty-two hundredths" or 0.22.

If you just write the problem using 22/100 for 22%, then you get the proportion ...

22/100 = 77/x

22x = 7700 . . . . . "cross multiply" (multiply by 100x)

x = 7700/22 = 350 . . . . divide by the coefficient of x

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If you're paying attention, you see that the solution of this kind of equation has the appearance that the denominator variable and the left-side value are simply swapped:

`0.22 = (77)/(x)\ \leftrightarrow\ x=(77)/(0.22)`

Effectively, we have multiplied both sides of the equation on the left by x/0.22. There is a property of equality that lets us do that. There is no such thing as a property of equality that says "swap with denominator." You must always pay attention to what is allowed by the properties of equality.